Question

How do I find the value of k​

Answer 1

The value of k is 2/5

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Further explanation

Vector is quantity that has magnitude and direction.

One example of a vector is acceleration.

Let us now tackle the problem !

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This problem is about Vector Diagram.

$\overrightarrow{OA} = \overrightarrow{a}$

$\overrightarrow{OC} = \overrightarrow{c}$

X is the midpoint of the line AC:

$\overrightarrow{x} = \frac{1}{2} (\overrightarrow{a} + \overrightarrow{c})$

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OC : CD = k : 1

$k \overrightarrow{CD} = \overrightarrow{OC}}$

$k( \overrightarrow{d} - \overrightarrow{c} ) = \overrightarrow{c}}$

$( \overrightarrow{d} - \overrightarrow{c} ) = \frac{1}{k} \overrightarrow{c}}$

$\overrightarrow{d} = \overrightarrow{c} + \frac{1}{k} \overrightarrow{c}}$

$\overrightarrow{d} = ( 1 + \frac{1}{k} ) \overrightarrow{c}}$

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$\overrightarrow{XD} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}$

$\overrightarrow{d} - \overrightarrow{x} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}$

$( 1 + \frac{1}{k} ) \overrightarrow{c} - \frac{1}{2} (\overrightarrow{a} + \overrightarrow{c}) = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}$

$( 1 + \frac{1}{k} - \frac{1}{2}) \overrightarrow{c} - \frac{1}{2} \overrightarrow{a} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}$

$( \frac{1}{k} + \frac{1}{2}) \overrightarrow{c} - \frac{1}{2} \overrightarrow{a} = 3 \overrightarrow{c} - \frac{1}{2} \overrightarrow{a}$

$\frac{1}{k} + \frac{1}{2} = 3$

$\frac{1}{k} = 3 - \frac{1}{2}$

$\frac{1}{k} = \frac{5}{2}$

$k = \frac{2}{5}$

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Learn more

• Velocity of Runner : brainly.com/question/3813437
• Kinetic Energy : brainly.com/question/692781
• Acceleration : brainly.com/question/2283922
• The Speed of Car : brainly.com/question/568302

Answer details

Grade: High School

Subject: Mathematics

Chapter: Vectors

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate, Stream , Vector